The Red Devils go into the match in sixth place in the table after a dramatic downturn in form, losing seven of their last nine matches in all competitions.
However, a win against Chelsea at Old Trafford would draw them level with the Blues on 67 points, and, according to The Sun, Solskjaer is convinced his squad can overtake them before the end of the season.
After losing to rivals Manchester City in midweek, the Norwegian coach tried to rouse his players and told them that he believes both Chelsea and Arsenal will choke in the run-in.
United have arguably the easiest run-in of the top-four rivals, taking on Huddersfield and Cardiff after the match against Chelsea.
The Blues, though, face two tricky games against Watford and Leicester City, with a Europa League semi-final against Frankfurt wedged in between.
Arsenal, likewise, have two European matches to contend with, while they also face difficult away trips to Leicester and Burnley, as well as a home clash against Brighton.